Intro Each of us has his or her own style of flyfishing. For some it might be a broad range of situations, for others it may be tightly defined. There are many factors that contribute to the ideal, some real, some imaginary. And from this there also is a favorite rod that comes to mind to fish these ideal waters. But as varied as the individuals so are the thoughts as to what characteristics make the perfect rod. As a rod maker I've been lead by my preferences in rod performance. The thought here is to report on what I have seen and how it was done, a guideline of sorts not necessarily for others to find the same results but as a basis for others to find and work up rod designs they prefer. A Fly Rod A simple definition of the function of a fly rod is that it is intended to transmit energy applied to it to a fly line. The line in turn extends to full length and comes to rest. Consequently, the fly rod needs to be made with sufficient material to structurally withstand the forces needed to allow the cast to occur without damage to the fly rod. And lastly, a fly rod should preform its function with a character that is preferred by the caster. Mr. Garrison's Idea In search of a rod design method, Mr Garrison decided to use his knowledge as an engineer. He set up a method of determining the moments(forces) created by the various weights of the line, bamboo, guides, and finish at locations through the length of a fly rod. To this he applied the character of a f(b) stress curve which was a different way of using that normal element of the material. Instead of using a fixed figure he chose to vary the value to either increase or decrease the flexure of the fly rod. His normal stress curve started with high values for the tip and gradually diminished the values through the length of the rod. This gave the greatest flexure to the tip and gradually stiffened the rod into the butt. A New Era Mr. Garrison developed his design ideas and mathematics in the late 20's and early 30's. During that era his only aids were paper and pencil and slide rule. Today even the simplest calculators can do the mathematics. Although, I'm told that one rod design still takes several evenings. That's right, I've never done a manual run through of the math. Having been computerized in the early 70's I saw Mr. Garrison's math as an ideal application. But even with a computer involved an understanding of the math is still needed. Action Length Because the fly rod is gripped by the hand most feel that the actual affect of the rod design ends at the cork grip. Consequently the action length, that part of the rod that actually has character, is the distance from the tip top to the top of the cork grip. Because the planing forms are set in 5 " increments a figure for the action length that is divisible by 5 is always chosen. Moments(forces) A moment is defined as a force attempting to cause rotation about a defined point. Where the direction of force and the arm of leverage are perpendicular. As an example consider tightening a nut with a wrench. Let's use these given factors. From the center of the nut to the center of the hand applying the force is 1' or 12". And the hand is applying a pressure of 1 lb or 16 oz. Then the moments of this example would be as follows: L X P = M 1' X 1# = 1 foot pound 1' X 16oz = 16 foot ounces 12" X 1# = 12 inch pounds 12" X 16oz = 192 inch ounces All of the above are correct calculations and terms. However for our purposes working with inch ounces will be the easiest. Inches to measure distance (L) and ounces to measure weight (P). Impact Factor Essentially this force is determined by the actual weight being hung off the tip of the fly rod multiplied by a safety factor. The weight is that of the fly line being fished and the weight of the tip top itself added together and expressed in ounces. This figure is then multiplied by 4 which is the safety factor. Understand Mr. Garrison's mathematics deals with static design. Static means that the elements are at rest. In real life a fly rod is a dynamic device it sees motion and other external forces other than that of just the static weights. To visualize this consider the fly line laying on the water surface. When the cast is started not only is the weight of the fly line being lifted but also the surface drag applied by the water contact. The 4 multiplier was derived at by tests that Mr. Garrison preformed. An Example At present, a fly line is classified by the weight (in grains) of the first 30' of the fly line. For a #4 weight fly line this is 120 grains. A standard tip top weights about 8 grains. Because we will be working in ounces these figures need to be converted into ounces. There are 437 grains per ounce. The tip impact factor would then be determined as follows: Line = 120/347 = .275 oz Tip Top = 8/437 = .018 oz _____ Total = .293 oz Factor x4 _____ Tip Impact 1.172 oz It isn't often that you may wish to design a rod at 30',the distance that all fly lines weights are standardized at, so another method is needed. A simple and fairly accurate method would be to simply weigh the entire fly line and then determine a weight per foot by dividing that total weight by the total length of the fly line. This value would be weight/foot which would then be multiplied by the line length desired. Tip Moments Once the tip impact is determined then the moments that the tip impact create can be calculated. For an action length let's imagine that we are designing a 7' 6" (90") rod. Together the normal handle and reelseat are 10". So the action length of a 7' 6" rod is 80". And because the planing forms are set at 5" increments the calculations of the tip impact would look as follows: tip (1.172 x 0) = 0.00 5" (1.172 x 5 = 5.860 10" (1.172 x 10) = 11.720 . . 80" (1.172 x 80) = 93.760 Line In Guides Moments To account for the line as it pass down the rod the center of gravity for each location needs to be determined. The center of gravity could be thought of as the balance point. An example would be if the point under investigation is 5" location then the center of gravity would be 2.5" because the line is of uniform weight. The line weight is calculated for the appropriate line size. Looking back to our other line example, if 30' of #4 weight line weighs 120 grains 1" weights .334 grains or .0008 oz. So the moments for the line on the rod would look as follows: tip (.0008 x 0 x 0 x 4) = .0000 5" (.0008 x 5 x 2.5 x 4) = .100 10" (.0008 x 10 x 5 x 4) = .160 . . . 80 (.0008 x 80 x 40 x 4) = 10.240 Varnish And Guide Moments Because of their diminished effect on the final results Mr. Garrison calculated these values one time and then used those figures as a standard on all future rod designs. Even with the added power of a computer it would be impractical to set up an alogarithm to come any closer that the graphed values Mr. Garrison used. Ferrule Moments The ferrule moments are calculated in the same fashion as the tip moments except that there is no weight until the ferrules. In our example if the 7'6"(90") rod is a 2 piece the ferrules are located at 45" so there would be no ferrule moments until that point. From experience a 7' 6" 2 piece rod require a size 13/64 ferrule which weighs 118 grains or .271 ounce. Again a impact factor is used (multiply x 4) therefore the calculations would be as follows: 45" (.271 x 0 x 4) = 0.000 50" (.271 x 5 x 4) = 1.355 . . 80" (.271 x 35 x 4) = 9.485 Center Of Gravity For those times that the ferrules aren't located on a 5" location then the center of gravity of their weight needs to be accounted for. Unlike the line that is off the rod the ferrules are a part of the rod and would use a length figure from the actual location to the location under investigation. Bamboo Moments These are the most complex to calculate and are of sufficient value to make those calculation worthwhile. I'm not going into all the mathematics of it all but just explain the concept. As you move from the tip to the butt of the rod the dimensions across the flats increase or the mass increases. Consequently a calculation to determine the center of mass is required to determine the location of the leverage arm for calculating the moments at each location. To start these values are of an imaginary rod. Then as the actual rod dimensions are derived then these values are substituted to bring the moments of the bamboo weight closer to their real life values. Total Moments With all the individual moments calculated their values are added together to reach total moments for each of the locations from the tip to the end of action length. Remember that these totals are only temporary that as new dimensions are generated then the moments are recalculated because of the changes in the bamboo moments. The Dimensions To determine the dimensions for the proposed rod design the total moments and the allowable stress values are placed into the following formula: Now as I have mentioned earlier these dimensions were only temporary and to bring them into more accurate values the bamboo moments are recalculated and then used with the allowable stress values to get a second value and then a third refiguring occurred. A valid question that can be raised is whether more times through the calculations would yield more accurate dimensions. Remember that in real life we are only working to be physically accurate to the nearest .001" and three derivations yield that mathematically. In Real Life Well on paper the stress curve Mr. Garrison developed had a smooth flow to it starting with a high value at the tip and gradually descending to lower values in the butt section. However, remember that the figured dimensions for the tip weren't used by Mr. Garrison. He considered these numbers to be unpractically small to make so he arbitrarily increased them and then blended the new tip dimension into the natural slope of the dimensional graph. But it is never mentioned in his writings what this did in real life to his stress curve. Well, by adding material he consequently lowered the f(b) values at the tip. Between The Lines It is another of those unmentioned items that sets the mind to wandering(wondering). But by simply rewriting the formula (I did it and I flunked rocket science - so I find it hard to believe that Mr. G had at some point in time) instead of solving for dimensions using stress values, stress values can be derived from dimensions. In the text that leads up to the explanation of the mathematics there is information that Mr. Garrison may have used an 8' Payne in developing his stress curves. Whatever the case the program I ended up with is bidirectional as far as stress values are concerned which can launch a person into discovering the ideas of rodmakers other than Mr. Garrison. All that is needed are the dimensions of a rod and to know at what distance that the castability of the rod is maximized. I suspect that some where there is a note book that would tell all. Program Accuracy It has been brought up that there are a few ever so slight differences in the program I wrote, Hexrod, and the way Mr. Garrison did his math. These differences are in the varnish and guide moments. To test to see how agreeable the two are I ran a side by side comparison to see. The test rod was the one that illustrates the math in his book. It might be pointed out that some of the deviation might be from slide rule versus computer syndrome. Mr.Garrison Hexrod delta .047 047 - .081 .081 - .104 .104 - .122 .122 - .136 .137 .001 .150 .151 .001 .163 .164 .001 .175 .177 .003 .188 .189 .001 .199 .201 .002 .213 .214 .001 .227 .228 .001 .241 .242 .001 .254 .255 .001 .268 .269 .001 .282 .282 - .296 .296 - As you can see the differences are small if any. But a better test might be the program against itself. A second test would be given the dimensions generated by the first run how close to the original stresses will the program come? Run #1 Run #2 196000 200838 196000 198957 189000 192663 184500 184546 180000 180010 175000 174825 170000 170980 167000 166210 164000 163895 161250 161417 158500 158655 156000 156115 153500 153333 151750 152362 150000 149668 148250 148819 146500 146605 Then the most important test of all. For a third test I reentered the stress values determined in the second run to see if I would get the same dimensions as what were input for the second test. There were no differences when carried out to the nearest thousands of an inch. Which proved to me at least against itself Hexrod could yield repeated and trustable results. I chose to forego any test which required digging out my K & E log - log slide rule. Revisited Garrison Curve As was mentioned earlier Mr. Garrison didn't adhere to the dimensions that he obtained for his tip dimensions. Instead he chose to alter the dimension upward to make it easier to make. Lets just for the sake of seeing look at what his stress curve would look like if he had plotted it with this tip alteration. Well the tip f(b) drops from the initial 196000 to just 51457. Onward I have only made one rod based on the Garrison tapers. Here again a personal preference. What I did was start miking rods and swapping tapers with other makers. The swapping part is reminiscent of a earlier stage of life involving baseball cards. With each newly obtained taper I would run the numbers through Hexrod to see what the character of the rod looked like stress curve wise. From this I narrowed down the different characters of rod tapers to those that I liked. Can I describe the action? Not really but I can show you the character graphically. Tip 45883 05 145740 10 171041 15 169797 20 171094 25 153944 30 150051 35 129181 40 133008 45 151417 50 150430 55 144962 60 145942 65 153009 A general description of the rod character would be that of a parabolic. But I seldom use that term because of the immediate association with what Mr. Garrison called a parabolic which tends to have a cooling effect in some cane rod circles. But with a little imagination you can see the distinct reversed 'J' of the curve which by most everyones definition is a parabolic action. softer tip, rigid mid section, & a softer butt. A reversed 'J' graph wise. Action Speed Because a rod action is a bit difficult to define I will also include a few graphs from other action rods just to perhaps add a little clarity. A classic fast action dry fly action would look like this. Tip 103543 05 283992 10 255838 15 268153 20 191826 25 189945 30 164611 35 181761 40 177543 45 177706 50 163416 55 151463 60 113423 65 108872 70 99021 75 91516 The rod listed above is perhaps one of the real classics. A 1920's Leonard Catskill 7'0" #2 weight.(Now how many quessed that one right ???) Here are a list of the numbers for those that would like them : Tip .043 05 .053 10 .070 15 .080 20 .100 25 .110 30 .125 35 .130 40 .140 45 .150 50 .165 55 .180 60 .210 65 .225 70 .230 74 .230 75 .245 76 .265 80 .265 84 .265 If you think about it for a minute it does make sense. A fast action rod has a very soft tip descending into a very strong butt as you can see in the numbers. Or as I refer to it a 'high amplitude' or f(b) range. And the reverse is also true a rod with 'low amplitude' or f(b) range would have a slow action. Why Stresses Not Dimensions? I am often asked this question when discussing rod tapers and alteration. As I pointed out earlier a f(b) curve only represents a character and only relates to makable numbers when a tip impact factor, number of sections, & such are applied. The character remains the same whether it is a 3 weight or a 4 weight, two piece or 3 piece. How ever if you were to look at the dimensions of these rods there is little in common to be able to alter with much success. Even if the compared rods are both the same number of pieces but different line weights the general 'slope' of the graphed dimensions will be different because of differing ferrule weights and bamboo weights. 6'3" 6'3" #3/2 #4/2 Tip .065 .070 .005 dif 05 .077 .082 10 .093 .100 15 .108 .116 20 .120 .128 25 .137 .146 30 .150 .160 35 .169 .179 40 .180 .191 45 .185 .196 50 .198 .209 55 .213 .224 60 .225 .236 65 .233 .244 .011 dif Things To Try Over the years some of what I think are the best casting rods were blended characters. By this I actually curve averaged two distinct f(b) curves from two rods creating a entirely new f(b) curve. The possibilities could be viewed as endless b † are certainly limits to all workable combinations. But rod design is not necessarily the myst that some make it out to be. A good start might be to graph known tapers that you have cast and know the feel of. Then perhaps you might design a 3 piece rod with the same character as a 2 piece that you are familiar with. Then move on to changing line sizes of rods that you have made. What you will find is that instead of just concentrating on which fly to pick next time on the stream you will start to think more about the character of the rod and its part of the big picture. The Next Step It may have been a presumption on my part but I advanced the cause by simply rewriting Mr. Garrison's formula and started solving for f(b) given dimensions. That way I could use his idea as a 'ruler' to investigate other existing rods for their stress characteristics. To determine a tip impact factor (weight of line hung off the rod tip) the rod under investigation would be cast and the distance at which the rod maximized was used as the value. This began to raise questions of how the energy was supposed to 'flow' through a fly rod. Some of what I thought to be the best casting rods had some of the most unusual stress curves. Beyond this, a stress curve only defines the character of a rod so by recalculating different line weights, and number of sections different rods were created with that same character.